Melez elektromanyetizma benzeri-parçacık sürü optimizasyon algoritması
Öz
Optimizasyon, bir problemin alternatif çözümleri içinden en uygununu seçme işlemidir. Optimizasyon
problemlerinin çözümü için, kabul edilebilir sürede optimuma yakın çözümler verebilen birçok sezgisel
optimizasyon algoritması önerilmiştir. Literatürde çok başarılı sezgisel optimizasyon algoritmaları bulunsa
da; tüm problemlerin çözümü için en optimum çözümü bulan algoritmalar henüz tasarlanmamıştır. Bu
yüzden yeni sezgisel optimizasyon algoritmaları önerilmekte ya da var olanların daha etkili çalışması için
öneriler sunulmaktadır.
Bu çalışmada, global optimizasyon için, Elektromanyetizma Benzeri (EM) algoritma ile Parçacık Sürü
Optimizasyon (PSO) algoritmasının birleşiminden oluşan yeni bir melez yöntem olan EM-PSO önerilmiştir.
Önerilen yöntemde, PSO algoritmasının hız denklemindeki sabit katsayılar yerine EM algoritmasındaki yük
ve toplam kuvvet değerleri kullanılmış ve EM algoritmasındaki parçacıkların hareketi bu denklem ile
gerçekleştirilmiştir. Önerilen yöntemin performansı beş farklı kalite testi fonksiyonu kullanılarak test
edilmiştir ve sonuçlar standart EM ve PSO algoritmalarının sonuçları ile karşılaştırılmıştır. Deneysel
sonuçlar, önerilen yöntemin standart EM ve PSO algoritmalarına göre daha başarılı olduğunu göstermiştir.
Anahtar Kelimeler
Hybrid electromagnetism like–particle swarm optimization algorithm
Abstract
Optimization is the process of selecting the most
appropriate solution in all alternative solutions of a
problem. A lot of meta-heuristic optimization
algorithms are proposed to find approximate
solutions for solving optimization problems in
acceptable time. Although there are many successful
meta-heuristic optimization algorithms in the
literature, an algorithm hasn’t been designed to find
optimum solutions for solving all optimization
problems yet. Therefore, new meta-heuristic
algorithms are proposed or the existing algorithms
are modified for better results. In this paper, a novel
hybrid optimization algorithm EM-PSO which is
consist of the Electromagnetism-like (EM) algorithm
and the Particle Swarm Optimization (PSO)
algorithm has been proposed for global
optimization.
The EM was firstly proposed by Birbil and Fang in
2003. The EM is inspired by attraction-repulsion
mechanism of electromagnetism theory. Each
member in the search space is considered as a
charged particle. The general algorithm consists of
four phases. These are initialization of algorithm,
local search, calculation of the total force, and
movement. In initialization phase, the particles are
initialized with random positions between the
corresponding upper bound and lower bound of the
search space. After, the objective function values of
the each particle are calculated. Finally, the best
objective function value is stored as x
best. In the
local search phase, local information about each
particle is gathered. In the calculation of the total
force phase, the charges of the each particle are
calculated according to their objective function
values. Then, the total force exerted on a particle
from other particles is calculated. In movement
phase, each particle is moved in the direction of the
total force by a random step length. If maximum
number of iterations is reached then algorithm
terminates. At the end of the algorithm, the best
particle is selected as the solution of the
optimization problem.
The PSO is proposed by Kennedy and Eberhart in
1995 which is an evolutionary computation
technique. The PSO was inspired from social
behaviors of bird and fish swarms. Each member in
the search space is considered as a particle. The
population is considered as a swarm. The PSO
algorithm focused on initializing and particle
movement. The particles are initialized with random
positions throughout the search space. Each particle
should consider the current position and its best
position (pbest). Moreover, each particle should
know the best position of the swarm (gbest). With
this information, the velocities of the each particle
toward its pbest and gbest are calculated. Then each
particle is moved by its velocity. If maximum number
of iterations is reached then algorithm terminates.
At the end of the algorithm, the best particle is
selected as the solution of the optimization problem.
In EM algorithm, each particle is only moved in the
direction of the total force. In EM-PSO algorithm,
the movement of particles in movement phase of EM
has been executed with PSO. The values q and F in
the EM have been used instead of the values c1, c2,
rand1 and rand2 in the velocity equation that is in
PSO. In this way, the movement of the each particle
is influenced by its best position (pbest) and the best
position of the swarm (gbest).
The performance of proposed hybrid EM-PSO
algorithm has been tested with five benchmark
functions which are Rastrigin, Rosenbrock, De Jong,
Griewang and Ackley. The obtained test results have
been compared with standard EM and standard PSO
algorithms’ test results. According to the all
benchmark test results we have showed that the new
proposed hybrid algorithm is successful than
standard EM and standard PSO.
In the future works, parallel and distributed versions
of EM-PSO algorithm can be developed.
Generalization of EM-PSO algorithm for multiobjective
optimization problems can also be one of
the further works
Keywords
